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Acyclic 5-choosability of planar graphs without small cycles

✍ Scribed by Mickaël Montassier; André Raspaud; Weifan Wang

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
188 KB
Volume
54
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A proper vertex coloring of a graph G = (V,E) is acyclic if G contains no bicolored cycle. A graph G is acyclically L‐list colorable if for a given list assignment L = {L(v): v: ∈ V}, there exists a proper acyclic coloring ϕ of G such that ϕ(v) ∈  L(v) for all v ∈  V. If G is acyclically L‐list colorable for any list assignment with |L (v)|≥ k for all v ∈  V, then G is acyclically k‐choosable. In this article, we prove that every planar graph G without 4‐ and 5‐cycles, or without 4‐ and 6‐cycles is acyclically 5‐choosable. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 245–260, 2007

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